Interactive Simulation of Elastic Deformable Materials

Martin Servin
Department of Physics, Umeå University, Sweden

Claude Lacoursiére
HPC2N/VRlab and Computing Science Department, Umeå University, Sweden

Niklas Melin
Department of Physics, Umeå University, Sweden

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Ingår i: SIGRAD 2006. The Annual SIGRAD Conference; Special Theme: Computer Games

Linköping Electronic Conference Proceedings 19:5, s. 22–32

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Publicerad: 2006-11-22


ISSN: 1650-3686 (tryckt), 1650-3740 (online)


A novel; fast; stable; physics-based numerical method for interactive simulation of elastically deformable objects is presented. Starting from elasticity theory; the deformation energy is modeled in terms of the positions of point masses using the linear shape functions of finite element analysis; providing for an exact correspondence between the known physical properties of deformable bodies such as Young’s modulus; and the simulation parameter. By treating the infinitely stiff case as a kinematic constraint on a system of point particles and using a regularization technique; a stable first order stepping algorithm is constructed which allows the simulation of materials over the entire range of stiffness values; including incompressibility. The main cost of this method is the solution of a linear system of equations which is large but sparse. Commonly available sparse matrix packages can process this problem with linear complexity in the number of elements for many cases. This method is contrasted with other well-known point mass models of deformable solids which rely on penalty forces constructed from simple local geometric quantities; e.g.; spring-and-damper models. For these; the mapping between the simulation parameters and the physical observables is not well defined and they are either strongly limited to the low stiffness case when using explicit integration methods; or produce grossly inaccurate results when using simple linearly implicit method. Validation and timing tests on the new method show that it produces very good physical behavior at a moderate computational cost; and it is usable in the context of real-time interactive simulations.

CR Categories: I.3.5 [Computer Graphics]: Physically based modeling—[I.3.7]: Computer Graphics—Virtual reality


deformable simulation; elasticity; constrained dynamics; stability; numerical integration


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